Study each of the growing geometrical patterns. Then do the following for each pattern. (I) Give a verbal description of how the pattern is growing. (ii)Set up a table of values.(III) Write down a numerical description for each pattern (you must relate the number of the frame to the number of figures in the frame). (IV) For each pattern, write down a formula that can be used to calculate the number of building blocks in any term. (v) Write down the value of the 10th frame. Use your formula to determine how many building blocks there are in the 100th frame of each growing pattern. M M Δ Δ Δ 2 (6) (6) (8) [40]​

Answers

Answer 1

A description of how the pattern is growing is that the pattern is growing by the addition of two blocks every time.

How to illustrate the pattern?

A numerical description of the pattern is:

1 - 2 blocks.

2 - 4 blocks.

3 - 6 blocks

4 - 8 blocks.

The formula that can be used to calculate the number if building blocks in any term will be 2n. For example, the number of blocks for the 5th term will be:

= 2n = 2 × 5 = 10

The value for the 10th frame will be:

= 2n

= 2 × 10 = 20

The value for the 100th frame will be:

= 2n

= 2 × 100 = 200

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Related Questions

What is the length of BC¯¯¯¯¯?

Answers

Answer:

meight you gotta do better then that

Step-by-step explanation:

a picture is probably necessary

Identifying Proportional Relationships


Which graph represents a proportional relationship?

Answers

Answer:

I can't answer this if you don't have the answer choices

I'm sorry

Identify the category to which the following statement belongs: Brandon has two weeks to decide on the topic of his research paper.
O Not important - Not Urgent
O Not Important - Urgent
O Important - Not Urgent
O Important-Urgent

Answers

Answer:

Important- not urgent

Step-by-step explanation:

The research paper is important but since Brandon has two weeks to decide it is not urgent.

Use the calculator to graph the function y = 2x2 25x + 3. What are the coordinates of the turning point of the graph to the nearest hundredth?

Vertex = (
,
)

Answers

The coordinates of the turning point of the graph of the quadratic equation is given by: (-6.25, -75.13).

What is the vertex of a quadratic equation?

A quadratic equation is modeled by:

[tex]y = ax^2 + bx + c[/tex]

The vertex is given by:

[tex](x_v, y_v)[/tex]

In which:

[tex]x_v = -\frac{b}{2a}[/tex][tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]

In this problem, the function is given by:

y = 2x² + 25x + 3.

Hence the coefficients are a = 2, b = 25, c = 3, then the coordinates of the vertex are given as follows:

[tex]x_v = -\frac{25}{2(2)} = -6.25[/tex][tex]y_v = -\frac{25^2 - 4(2)(3)}{4(2)} = -75.13[/tex]

The coordinates of the turning point of the graph of the quadratic equation is given by: (-6.25, -75.13).

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Answer:

6.25, -75.13

Step-by-step explanation:

it just is

Flying against the wind, an airplane travels 2520 kilometers in 4 hours. Flying with the wind, the same plane travels 9450 kilometers in 9 hours. What is the rate of the plane in still air and what is the rate of the wind?

Answers

Using the relation between velocity, distance and time, it is found that:

The rate of the plane is of 840 km/h.The rate of the wind is of 210 km/h.

What is the relation between velocity, distance and time?

Velocity is distance divided by time, that is:

[tex]v = \frac{d}[t}[/tex]

Flying against the wind, an airplane travels 2520 kilometers in 4 hours, that is:

[tex]v - v_w = \frac{2520}{4}[/tex]

[tex]v - v_w = 630[/tex]

[tex]v = 630 + v_w[/tex]

Flying with the wind, the same plane travels 9450 kilometers in 9 hours, hence:

[tex]v + v_w = \frac{9450}{9}[/tex]

[tex]v + v_w = 1050[/tex]

[tex]v = 1050 - v_w[/tex]

Hence, solving for the wind's speed:

[tex]630 + v_w = 1050 - v_w[/tex]

[tex]2v_w = 420[/tex]

[tex]v_w = \frac{420}{2}[/tex]

[tex]v_w = 210[/tex]

For the plane, we have that:

v = 1050 - 210 = 840.

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Help please I need asap

Answers

Answer: -120

Step-by-step explanation:

[tex]2\sum^{4}_{p=1} (p^{2}-9p)=2[(1^{2}-9(1))+(2^{2}-9(2))+(3^{2}-9(3))+(4^{2}-9(4))]=\boxed{-120}[/tex]

The table below shows the amount of money spent on skin diving and scuba equipment in some recent years.
Skin Diving and Scuba Equipment

Year
Sales ($millions)
1993
315
1994
322
1995
328
1996
340
1998
345
1999
363

Let x represent the year and y represent the amount of sales, in millions of dollars, in the regression equation.
y = 7.36 x minus 14,354.33,
Use the regression equation to predict the sales of skin diving and scuba equipment in the year 2008.
a.
44,000,000
b.
440,000,000
c.
42,455,000
d.
424,550,000



Please select the best answer from the choices provided


A
B
C
D
Mark this and return

Answers

The sales of skin diving and scuba equipment in the year 2008 is (d) 424,550,000

How to predict the sales in 2008?

The regression equation is given as;

y = 7.36x - 14,354.33

In 2008, the value of x is

x = 2008

So, we have:

y = 7.36 * 2008 - 14,354.33

Evaluate

y = 424.55

Hence, the sales of skin diving and scuba equipment in the year 2008 is (d) 424,550,000

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The sales of skin diving and scuba equipment in the year 2008 is (d) 424,550,000.

We have given that,

The table below shows the amount of money spent on skin diving and scuba equipment in some recent years.

How to predict the sales in 2008?

The regression equation is given as

y = 7.36x - 14,354.33

In 2008, the value of x is

x = 2008

So, we have y = 7.36 * 2008 - 14,354.33

Evaluate y = 424.55

Hence, the sales of skin diving and scuba equipment in the year 2008 is (d) 424,550,000

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The fox population in a certain region has a continuous growth rate of 7 percent per year. It is estimated that the population in the year 2000 was 15000.

(a) Find a function that models the population
t
years after 2000 (
t
=
0
for 2000).
Your answer is
P
(
t
)
=




(b) Use the function from part (a) to estimate the fox population in the year 2008.
Your answer is (the answer must be an integer)

Answers

There are 25773 foxes in the region in the year 2008

How to determine the function?

The given parameters are:

Initial value, a = 15000Rate, r = 7% or 0.07

Let the number of years after 2000 be x.

So, the function is

f(x) = a * (1 + r)^x

This gives

f(x) = 15000 * (1 + 0.07)^x

In 2008, we have:

x = 8

So, the equation becomes

f(8) = 15000 * (1 + 0.07)^8

Evaluate

f(8) = 25773

Hence, there are 25773 foxes in the region in the year 2008

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write an exponential expression that shows (10 to the power of 4) to the power of 4 simplified

Answers

Answer: it could be

[tex](10^{4} ) ^{4}[/tex]

Step-by-step explanation:

What is true of an equilateral triangle? Two of its side lengths are equal. All its side lengths are equal. None of its side lengths are equal. None of its interior angles are equal. What is true of an equilateral triangle ? Two of its side lengths are equal . All its side lengths are equal . None of its side lengths are equal . None of its interior angles are equal .​

Answers

Answer:

All its side lengths are equal

(and all the agle of 60°)

Step-by-step explanation:

What is true of an equilateral triangle? Two of its side lengths are equal. All its side lengths are equal. None of its side lengths are equal. None of its interior angles are equal. What is true of an equilateral triangle ? Two of its side lengths are equal . All its side lengths are equal . None of its side lengths are equal . None of its interior angles are equal .​

Separable differential equation
y’ln^2y+ysqrtx=0 y(0)=e

Answers

By applying the theory of separable ordinary differential equations we conclude that the solution of the differential equation [tex]\frac{dy}{dx} \cdot (\ln y)^{2} + y\cdot \sqrt{x} = 0[/tex] with y(0) = e is [tex]y = e^{\sqrt [3]{-2\cdot x^{\frac{3}{2} }+1}}[/tex].

How to solve separable differential equation

In this question we must separate each variable on each side of the equivalence, integrate each side of the expression and find an explicit expression (y = f(x)) if possible.

[tex]\frac{dy}{dx} \cdot (\ln y)^{2} + y\cdot \sqrt{x} = 0[/tex]

[tex](\ln y)^{2}\,dy = -y \cdot \sqrt{x}\, dx[/tex]

[tex]-\frac{(\ln y)^{2}}{y}\, dy = \sqrt{x} \,dx[/tex]

[tex]-\int {\frac{(\ln y)^{2}}{y} } \, dy = \int {\sqrt{x}} \, dx[/tex]

If u = ㏑ y and du = dy/y, then:

[tex]-\int {u^{2}\,du } = \int {x^{\frac{1}{2} }} \, dx[/tex]

[tex]-\frac{1}{3}\cdot u^{3} = \frac{2\cdot x^{\frac{3}{2} }}{3} + C[/tex]

[tex]u^{3} = -2\cdot x^{\frac{3}{2} } + C[/tex]

[tex](\ln y)^{3} = - 2\cdot x^{\frac{3}{2} } + C[/tex]

[tex]C = (\ln e)^{3}[/tex]

[tex]C = 1[/tex]

And finally we get the explicit expression:

[tex]\ln y = \sqrt [3]{-2\cdot x^{\frac{3}{2} }+ 1}[/tex]

[tex]y = e^{\sqrt [3]{-2\cdot x^{\frac{3}{2} }+1}}[/tex]

By applying the theory of separable ordinary differential equations we conclude that the solution of the differential equation [tex]\frac{dy}{dx} \cdot (\ln y)^{2} + y\cdot \sqrt{x} = 0[/tex] with y(0) = e is [tex]y = e^{\sqrt [3]{-2\cdot x^{\frac{3}{2} }+1}}[/tex].

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Need the answer for number 3 please!!!!

Answers

Answer:

Perimeter = 2(l + b)

= 2(x + 5x³ + 4 - x²)

= 2x + 10x³ + 8 - 2x²

= 10x³ - 2x² + 2x + 8

Hence, ur answer is the first option.

Answer:

A.

Step-by-step explanation:

L = x

W = 5x³ + 4 - x²

P = 2L + 2W

P(x) = 2x + 2(5x³ + 4 - x²) = 2x + 10x³ + 8 - 2x²

P(x) 10x³ - 2x² + 2x + 8

L = x

W = 5x³ + 4 - x²

P= 2L + 2W

P(x) = 2x + 2(5x³ + 4 - x²) = 2x + 10x³ + 8 - 2x²

= P(x) 10x³ - 2x² + 2x + 8

What is the value of 6¹?
6° = 1
6 = 6
6 = 36
6 = 216

A.220
B.240
C.864
D.1,296

Answers

Answer: D

Step-by-step explanation:  

6^4 = 6 x 6 x 6 x 6 = 1,296

6^4 = 1,296

Analyze the conditional statement below and complete the instructions that follow.
If an angle measures 90°, then it is a right angle.
Identify ~q.
O An angle does not have measure 90°.
OIt is not a right angle.
An angle measures 90°.
OIt is a right angle.

Answers

Answer: It is not a right angle.

Need help anyone please!!!

Answers

the picture is blurred

What is the present value of a cash inflow of 1250 four years from now if the required rate of
return is 8% (Rounded to 2 decimal places)?

Answers

Using simple interest, it is found that the present value of the cash inflow is of 947.

Simple Interest

Simple interest is used when there is a single compounding per time period.

The amount of money after t years in is modeled by:

A(t) = A(0)(1 + rt)

In which:

A(0) is the initial amount.r is the interest rate, as a decimal.

In this problem, the parameters are given as follows:

r = 0.08, t = 4, A(t) = 1250.

We have to solve for A(0) to find the present value, hence:

A(t) = A(0)(1 + rt)

1250 = A(0)(1 + 0.08 x 4)

A(0) = 1250/1.32

A(0) = 947.

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A hose fills a hot tub at a rate of 5.2 gallons per minute. How many minutes will it take to fill a 600 gallon hot tub? (nearest tenth)

Answers

Answer:

115.38 is what I got when I tryed to work it out

A line has slope Four-thirds. Through which two points could this line pass?

Answers

Answer:

Two points this line can pass through (1, 4/3) and (2, 8/3)

Step-by-step explanation:

The equation of the line is written in the slope-intercept form,

y = mx + b

where m represents the slope

          b represents the y-intercept

where the format of a point is (x, y)

Given:

slope = 4 / 3equation: y = 4/3x

we can plug in a number for x to find y

when x = 0,

y = 4/3(0)

y = 0

point: (0,0)

when x = 1,

y = 4/3(1)

y = 4/3

point: (1, 4/3)

when x = 2,

y = 4/3(2)

y = 8/3

point: (2, 8/3)

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A manufacturer of pacemakers wants the standard deviation of the lifetimes of the batteries to be less than 1.8 months. A sample of 20 batteries had a standard deviation of 1.6 months. Assume the variable is normally distributed. Find the 95% confidence interval of the standard deviation of the batteries. Based on this answer, do you feel that 1.8 months is a reasonable estimate?

Answers

Answer:

Look down my answer↓:

Step-by-step explanation:

Line l passes through point (−2,37) and line p is the graph of y+3=−5(x+4) .

If l is parallel to p what is the equation of l ?

Answers

The slope of line p is -5, so substitute into point-slope form, we get

[tex]\boxed{y-37=-5(x+2)}[/tex]

10 points need help finding area

Answers

Answer:

8 un^2

Step-by-step explanation:

to find this answer you must find the area of the rectangle and then the triangle

the rectangles area is

2 * 3 = 6 un^2

the traingle is

2 * 2 * 1/2 = 2 un^2

now you add them

6 + 2 = 8 un^2

Area is 8.:)))))))))))))

Which statement is true about the end behavior of the graphed function?

Answers

Step-by-step explanation:

both ends are going to the same direction so the degree is even. the right side is going up so the leading coefficient is positive.

(h+k)(1) is
(k-h)(4) is
(k/h)(3) is
(h•k)(0) is
(k •h)(0) is
(h•k)(3) is
h(k(-2))

Answers

Answer:

Step-by-step explanation:

(h+k)(1)=h(1)+k(1)=2+(-1)=2-1=1

(k-h)(4)=k(4)-h(4)=0-(-1)=1

(k/h)(3)[tex]=\frac{k(3)}{h(3)} =\frac{-1}{0} =- \infty[/tex]

(h.k)(0)=h(0).k(0)=3(-2)=-6

(k.h)(0)=k(0).h(0)=-2(3)=-6

(h.k)(3)=h(3).k(3)=0(-1)=0

h(k(-2))=h(-3)=0

Determine whether it is a function

Answers

Answer:

Relation 3 is not a function, as s has two outputs: tree and desk. Relation 4 is not a function for the same reason. -1 has three outputs: -2, -4, and -7.

find the roots of x^4-1=0​

Answers

Answer:

x = +1

x = -1

Step-by-step explanation:

x^4-1=0​

x^4=+1​

fourth root of x^4= fourth root of +1​

x = +1

x = -1

Solve the system of equations by graphing.

y = x − 6
3x − 3y = 18

Answers

Solving the equation,

X = 6

Y = (-6)

P(-4, 6), Q(2, 5), R(3, -1), S(-3, 0)

Use slope to determine whether the following is a parallelogram. Explain why or why not.

Find the slope of PQ
Find the slope of QR
Find the slope of RS
Find the slope of SP
Use this information to determine if the quadrilateral a parallelogram.

Answers

From the slopes it is confirmed that PQ || RS OR|| SP and therefore it is a parallelogram .

What is a Parallelogram ?

A parallelogram is a quadrilateral in which the opposite sides are parallel.

The coordinates of a quadrilateral is given

To prove that it is a parallelogram

PQ || RS

OR|| SP

The slope of a straight line is given by

[tex]\rm m = \dfrac{y_2 -y_1}{x_2- x_1}[/tex]

For PQ

m = (-1/6) = -1/6

For QR

m = -6/1 = -6

For RS

m = 1/(-6) = -1/6

For SP

m = -6

From the slopes it is confirmed that

PQ || RS

OR|| SP

and therefore it is a parallelogram

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If f(x) = 3x-2 and g(x) = x+²,
find f(g(x)).
f(g(x)) = [?]
Simplify your answer as much as possible.

Answers

Answer:

x

Step-by-step explanation:

[tex]f(g(x)) = 3(\frac{x+2}{3} )-2\\= x + 2 - 2\\= x[/tex]

1. EL precio a la venta de una impresora de inyección de tinta es de $285.000 incluida una Ganancia del 35%. ¿cuánto le cuesta a la tienda cada impresora?

Answers

Excluyendo el componente de ganancia del coste para el consumidor según (1), la impresora tuvo un coste de $ 211.111,11 para el vendedor.

¿Cómo encontrar el precio de una impresora sin ganancia?

En el enunciado tenemos el precio de una impresora para el consumidor, el cual comprende el dinero invertido por vendedor más la ganancia esperada. Este indicador observa la siguiente fórmula:

C' = C · (1 + r/100)     (1)

Donde:

C - Coste asumido por el vendedor, en unidades monetarias.C' - Coste para el consumidor, en unidades monetarias.r - Tasa de ganancia, en porcentaje.

Si sabemos que C' = $ 285.000 y r = 35 %, entonces el coste asumido por el vendedor es:

285.000 = 1,35 · C'

C' ≈ 211.111,11

Excluyendo el componente de ganancia del coste para el consumidor según (1), la impresora tuvo un coste de $ 211.111,11 para el vendedor.

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4 Pencils and 2 rulers cost $8. 2 pencils and 4 rulers cost $10. Find the cost of 3 rulers and 3 pencils

Answers

Answer:

$9

Step-by-step explanation:

Let, the price of pencils is x, and the price of rulers is y.

4x+2y=8.....(i)

2x+4y=10......(ii)

From eq(i),

2(2x+y)=8

2x+y=4

y=4-2x eq(iii)  .....put in eq(ii)

2x+4(4-2x)=10

2x+16-8x=10

-6x=10-16

x=-6/-6

x=1 put in eq (iii)

y=4-2(1)

y=2

Now, the price of 3 rulers and 3 pencils = 3x+3y=3(1)+3(2)

=9

Please give me brainlist.

We can convert the statements into quadratic equations, which is not a big thing. In simple words, the equation which includes 2 unknowns. We can sustitute with x & y for the simplicity.

Let assume the price of pencil is x and the price of rulers is y. While doing the operations we can remove the units which is $ (for price).


So now we can rewrite the first statement as 4x + 2y = 8.
As everything is dividant of 2, I'm simplifying the eqution by dividing everything by 2.

So, 2x + y = 4 ----(1)

Similarly the second statement is, 2x+4y = 10.

So, 2x + 4y = 10 ----(2).

To solve this we need to make any of the variable (either x or y) zero. We can do that in multiple ways, Here I am trying to make the x =0 by substrating equation 1 from equation 2.

2x + 4y = 10 -
2x + y = 4
___________

-0 + 3y = 6

3y = 6

So y= 6/3=2

Now we have the value of y, to find x apply it in any eqution that has x

I'm applying it in eqution 2

2x + 2 = 4
2x = 2
x=1

Now we want to value the cost of 3 rulers and 3 pencils

3x + 3y = 3(1) + 3(2) = 3 + 6 = 9

So

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